Lesson 18 · The box shape - Build a Physics Engine

The box shape

The second shape is an axis-aligned box, described by how far it reaches from its center along each axis. Today you build it and its bounding box, which for a box is itself.

The goal

Define an axis-aligned box shape by its half-extents and compute its bounding box around a center.

Start here - the target

TO DO

Scenario: The bounds of an axis-aligned box

Givena box with half-extents {2, 1} centered at {0, 0}

Whenits bounding box is computed

Thenthe box has Min {-2, -1} and Max {2, 1}

Andthe same box centered at {3, 0} has Min {1, -1} and Max {5, 1}

Background

An axis-aligned box is described by its half-extents: how far it reaches from its center toward an edge along each axis. A box with half-extents {2, 1} is 4 wide and 2 tall, spanning from {-2, -1} to {2, 1} around the origin. Storing half-extents rather than a width and height makes the math symmetric - the corners are just the center plus and minus the half-extents - which is why engines favor this form.

For an axis-aligned box the bounding box is the box, so Bounds is trivial today. It earns its own shape type because axis-aligned boxes collide with a fast, dedicated overlap test you will write in the next chapter, without the general machinery that rotated polygons need. Keep boxes upright for now; when you want a tilted rectangle, that is the convex polygon coming two lessons from now.

Make it work

// half-extents: distance from center to an edge along each axis
type Box struct{ HalfExtents Vec2 }
func (bx Box) Bounds(center Vec2) AABB {
  return AABB{Min: Sub(center, bx.HalfExtents), Max: Add(center, bx.HalfExtents)}
}

CheckpointDONE

A box shape knows its bounding box. Commit and stop here.